A critical parameter in rigid disk drive design is the height or gap between the read-write slider and the magnetic medium. The flying height is below 50 nm at the present state of the art, but because the height is not easily measured directly, the exact value is difficult to determine in an assembled drive. For this reason, the Data Storage Industry relies on optical testers for quantifying flying height in production and in developing new designs as explained in, for example, B. Bhushan, Tribology and Mechanics of Magnetic Storage Devices (New York: Springer-Verlag, 1990) pp. 765-797.
Optical testers employ a rotating, transparent glass substrate or surrogate disk in place of the magnetic disk and determine the flying height by analysis of interference phenomena between the slider and the glass as described in, for example, W. Stone, "A proposed method for solving some problems in lubrication" The Commonwealth Engineer, (Nov. 1921 and Dec. 1921); J. M. Fleischer and C. Lin, "Infrared laser interferometer for measuring air-bearing separation," IBM J. Res. Develop. 18 (6), 529-533 (1974); T. Ohkubo and J. Kishegami, "Accurate Measurement of Gas-Lubricated Slider Bearing Separation using Laser Interferometry," Trans. ASME, Vol 110, pp 148-155 (Jan. 1988); C. Lacey, J. A. Adams, E. W. Ross, and A. Cormier, "A new method for measuring flying height dynamically," Proc. DiskCon '92 (1992), pp.27-42; and T. E. Erickson and J. P. Lauer, "Multiplexed laser interferometer for non-dispersed spectrum detection in a dynamic flying height tester," U.S. Pat. No. 5,673,110 (Sep. 30, 1997).
However, the exact flying height of a slider in an optical tester is often not known to an adequate degree of precision due in part to variations in the optical properties of the slider material, including most specifically, the real and imaginary parts of the effective complex index of refraction. These quantities, commonly known as the optical constants n and k, play an important role in calculating the absolute flying height. Traditionally, an ellipsometer measures the optical constants of a material, and the results are entered by hand into the flying-height test software. In practice, the ellipsometric geometry is very different from that of typical flying-height testers, so a completely separate instrument is used for this purpose.
The independent measurement of optical constants is a significant burden in optical flying-height testing. Furthermore, uncertainty in the values of n and k related to infrequent or incorrect ellipsometric analysis introduces systematic errors of several nm. These errors are often invisible to instrument qualification screens such as system to system correlation, repeatability and reproducibility. Thus, it is possible to have self-consistent flying height data that is also consistently inaccurate.
Ideally, a flying-height tester incorporates means to determine the optical constants in situ, for every slider under test. To achieve this ideal, a flying-height test geometry is proposed herein involving an oblique angle of incidence and a high-speed homodyne interferometric receiver. As will be seen, ellipsometry and radiometry are applied directly to the flying height problem by treating the air gap as a dynamic thin film (See, e.g., P. de Groot, L. Deck, J. Soobitsky, J. Biegen, "Polarization interferometer for measuring the flying height of magnetic read-write heads," Opt. Lett. 21 (6), 441-443 (1996); P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat and J. Soobitsky, "Polarization interferometer for flying height testing," Proc. IDEMA Future Dimensions in Storage Symposium, 89-94 (1997); and P. de Groot, "Optical gap measuring apparatus and method" U.S. Pat. No. 5,557,399 (1996)).
This technique is referred to as polarization interferometry to distinguish it from the classical null ellipsometer with its rotating waveplates and polarizers. A significant benefit of polarization interferometry is that there is sufficient information to solve for n and k as part of the flying height test procedure. The present invention describes how n and k are calculated and also provides an estimate of uncertainty and its effects on the final flying height.
As mentioned above, the optical constants of sliders play an important role in the precise determination of flying height. Muranushi, Tanaka and Takeuchi were the first to describe in detail the importance of including the optical properties of slider materials in optical flying height testing (F. Muranushi, K. Tanaka, and Y. Takeuchi, "Estimation of zero-spacing error due to a phase shift of reflected light in measuring a magnetic head slider's flying height by light interference" Adv. Info. Storage syst., 4, 1992, p.371). The same paper was presented at the ASME Winter Annual Meeting, Atlanta, Ga. (1991).
The fundamental issue is the phase shift that occurs at the slider air-bearing surface (ABS) upon reflection. In a conventional flying height tester, there is no way to distinguish between a phase shift on reflection and the actual gap between the slider and the ABS. Muranushi et al. refer to this problem as zero spacing error or ZSE. As is shown in Table 1 below, the ZSE can be as large as 20 nm, which is the same magnitude as the flying height of modern high-performance sliders (The calculations for Table 1 also appear in the paper "Interferometric measurement of disk/slider spacing: The effect of phase shift on reflection," by C. Lacey, R. Shelor, A. Cormier and R. E. Talke, IEEE Trans. Magn. MAG-29 (6) (1993)).
TABLE 1 ______________________________________ Theoretical zero-spacing error .DELTA.h attributable to the material phase change on reflection of Al.sub.2 O.sub.3 --TiC at three different wavelengths. .lambda. (nm) n k .DELTA.h (nm) ______________________________________ 405 2.15 0.55 8.8 633 2.14 0.47 12.1 830 2.13 0.61 20.1 ______________________________________
It is therefore critical to characterize and correct for the optical properties of the ABS, which vary with material composition and structure.
The most common material for the body and ABS of read-write sliders is an amalgam of alumina (Al.sub.2 O.sub.3) and titanium carbide (TIC). Under an optical microscope, the polished ABS shows grains of brightly-reflecting TiC imbedded in alumina. The grains are typically a few microns in width, and a scanning-probe microscope reveals that the TiC is raised several nm above the alumina. A light beam incident on such a surface diffracts into a broad range of angles, with a resultant amplitude and phase that depends strongly on the size, distribution and relative surface height of the TiC. The apparent reflectivity of such a surface depends therefore on the surface structure, angle of incidence and numerical aperture of the imaging optics.
Given the material complexity of the ABS surface, it is not easy to predict its optical properties. It has become common practice in flying-height testing to model the complicated physical structure of TiC as a smooth, homogeneous material, for which it is possible to calculate the reflected electric field using a single, complex index of refraction. This simplified model assumes that the effective n and k measured by an ellipsometer are sufficient to estimate the complex reflectivity of the ABS for any optical system, including any material-dependent phase shifts.
Assuming that it is meaningful to define an effective n and k of the slider ABS, the complex reflectivity for s and p polarized light follow from the Fresnel equations (M. Born and E. Wolf, "Principles of Optics" (Pergamon Press) p. 40): ##EQU1## Here .phi. is the angle of incidence and .phi. is the (complex) angle of refraction. The angles are related by Snell's law: EQU n sin(.phi.)=sin(.phi.), (2.)
where EQU n=n+ik, (3.)
is the effective complex refractive index of refraction, found by performing conventional ellipsometry (Following Born and Wolf, we prefer to use the n+ik definition of the complex index, rather than the more common n-ik). The Fresnel Eqs. (1) and (2) are the starting point for the theoretical estimates of ZSE presented in Table 1.
In reality, Eqs.(1) and (2) are only approximately true, because of the heterogeneous nature of the slider material. For example, it should be possible to calculate the intensity reflectivity at normal incidence using the formula: ##EQU2##
This is an easy result to check experimentally, by simply measuring the incident and reflected intensities for a Helium Neon laser beam. Results of such an experiment using the same laser and small-aperture collection optics for both 50.degree. ellipsometry and normal-incidence reflectance measurements are reported in Table 2 for several different types of Al.sub.2 O.sub.3 -TiC and show that the calculated R using the effective n and k are consistently wrong, by about 20%. This error indicates that the simple n and k model is not entirely satisfactory for heterogeneous materials such as Al.sub.2 O.sub.3 -TiC.
Although there are clear deficiencies in the n and k model, evidence suggests that this simplification is still useful and considerably better than ignoring material effects altogether. The theory calculations in Table 2 below have the wrong absolute magnitudes, but nonetheless properly rank the sample materials according to their relative reflectivities.
TABLE 2 ______________________________________ Intensity reflectivity of four Al.sub.2 O.sub.3 --TiC samples compared with the theoretical predictions using n and k. Ellipsometry Reflectivity n k theory measured ______________________________________ 2.16 0.40 0.148 0.122 2.22 0.43 0.157 0.127 2.19 0.56 0.165 0.132 2.37 0.54 0.185 0.144 ______________________________________
There is also ample evidence to suggest that the ZSE is correlated to the effective optical constants. For these reasons, Muranushi et al. (supra) proposed ellipsometric analysis as a means of characterizing slider materials for optical flying height testing. Their approach has become accepted standard practice in the measurement procedures of commercial test equipment (e.g., R. Pavlat "Flying height measurement systems and slider absorption", IDEMA Insight 7 (5), p.1 (1994); Y. Li, "Flying height measurement on Al.sub.2 O.sub.3 film of a magnetic slider," Proc. ASME/STLE Joint Tribology Conference. Paper 96-TRIB-61 (1996); and K. Lue, C. Lacey and F. E. Talke, "Measurement of flying height with carbon overcoated sliders," IEEE Trans. Magn. 30 (6), 4167-4169 (1994))
Whatever the limitations of the n and k model, once it is accepted as a useful and meaningful approximation, it seems sensible to combine the role of the ellipsometer with that of the flying height tester to reduce the measurement errors attributable to infrequent or incorrect ellipsometric analysis. Consequently, one of the objects of this invention has been to develop an optical sensing technology that measures the effective optical constants n and k of sliders during flying height testing. As will be shown, this is achieved by analysis of the polarization state of light reflected from the slider-glass interface.
Other objects of the invention will in part be obvious and in part appear hereinafter when the detailed description to follow is read in connection with the various figures.